In recent years, the world has witnessed explosive growth in the demand for wireless communications and it is predicted that this demand will continue to increase in the future. There are well over 500 million users that subscribe to cellular telephone services and the number is continually increasing. Eventually, in the not too distant future the number of cellular subscribers will exceed the number of fixed line telephone installations. Already, in many cases, the revenues from mobile services already exceeds that for fixed line services even though the amount of traffic generated through mobile phones is much less than in fixed networks.
Other related wireless technologies have experienced growth similar to that of cellular. For example, cordless telephony, two-way radio trunking systems, paging (one way and two way), messaging, wireless local area networks (WLANs) and wireless local loops (WLLs). In addition, new broadband communication schemes are rapidly being deployed to provide users with increased bandwidth and faster access to the Internet. Broadband services such as xDSL, short-range high-speed wireless connections, high rate satellite downlink (and the uplink in some cases) are being offered to users in more and more locations.
It is well known that the performance of a communications receiver operating over a fading channel (i.e. mobile radio channels, etc.) can be improved by the use of channel equalization which in turn can be improved by use of whitening matched filtering. In a conventional receiver structure the Intersymbol Interference (ISI) is mitigated by channel equalization. Schemes commonly employed to mitigate ISI include full maximum likelihood sequence estimation (MLSE), finite-length decision feedback equalization (DFE), maximum a posteriori (MAP) equalization, a type of MLSE equalization known as soft output Viterbi algorithm (SOVA) equalization, reduced state sequence estimation (RSSE) or any other suitable equalizer wherein the equalizer is preferably (or required to be in come cases) preceded by a whitening matched filter (WMF).
It is common for the WMF to be implemented as a cascade of the T/2 spaced channel matched filter, a decimator to symbol rate 1/T followed by a T-spaced whitening filter. The optimum matched filter in the case of AWGN or flat fading channels, in the sense that the decimated matched filter output is a sufficient statistic for symbol-by-symbol detection as rate 1/T, has been found to be the filter matched to the partial T-spaced transmitting pulse shape or the T/2-spaced pulse followed by a decimator to symbol rate 1/T. In the presence of ISI, the decimated output of the matched filter, matched to the channel by convolving the pulse shape with the channel impulse response, is also an optimal sufficient statistic for detection at rate 1/T. The matched filter, however, does not remove ISI but rather concentrates the maximal symbol energy in the correct sampling instance. The T-spaced whitening filter subsequently attempts to effectively cancel the noncausal precursor ISI by replacing the samples and channel by their minimal phase equivalents (See H. Meyr, “Digital Communication Receivers: Synchronization, Channel Estimation and Signal Processing,” John Wiley & Sons, Inc., 1998, Section 13.3.4).
The performance of many equalization techniques commonly known and used today is sensitive to channel phase. For example, reduced state sequence estimation (RSSE) is a well-known equalization technique whose best performance is obtained for minimum phase channels. For non-minimum phase channels, the performance of a RSSE based equalizer may not be adequate. Channel estimation is aided, for example in GSM systems, by the insertion of a training sequence in the midamble of the burst. Equalization is then performed in different directions over the left and right data fields. Therefore, the effect on equalization of the minimum phase part of the channel response in one direction is equivalent to the effect on equalization of the maximum phase in the other direction. It is well known that the RSSE equalization performs poorly in non-minimal phase conditions.
Thus, the use of a WMF is beneficial, if not critical, to the performance of a communications receiver structure that incorporates the above mentioned equalization technique, especially RSSE type equalization techniques, and that is intended to operate with fading channels such as mobile radio channels, cellular, broadband, etc. described above.
A drawback of the above described mobile radio system is the computational complexity involved in determining the transfer functions of the matched filter and whitening filter components of the WMF. Most prior art techniques implement the whitening filter as a FIR filter (i.e. moving average or MA type filter) which requires very long tap lengths to achieved adequate performance. Other prior art approaches employ open-ended iterative search techniques to determine the FIR filter coefficients. The computational requirements of these open-ended iterative search techniques cannot be predicted.
It is desirable, therefore, to have a technique for determining the matched filter response and the whitening filter response of a WMF that has low computational complexity and involves a constant number of computations.